U.S. Bureau of Labor Statistics

Employee Benefits Survey

Technical Information about Standard Errors for Retirement Benefit Estimates for State and Local Government Workers, 2007

To assist users in ascertaining the reliability of National Compensation Survey retirement benefit estimates for State and local government workers, standard errors of estimates are made available. Standard errors provide users a tool to judge the quality of an estimate to ensure that it is within an acceptable range for their intended purpose. These standard errors are available in PDF format on the webpage, Tables of Standard Errors for Retirement Benefit Estimates for State and Local Government Workers, 2007.

The estimates are derived from a sample survey and thus are subject to sampling errors. Sampling errors are differences that occur between the results computed from a sample of observations and those computed from all observations in a population. Estimates derived from different samples selected using the same sample design may differ from each other. (In this case, the population of an estimate is a worker characteristic, establishment characteristic, or geographic area.)

The standard error is a measure of the variation among these differing estimates. It can be used to measure the precision with which an estimate from a particular sample approximates the expected result of all possible samples. The standard errors can be used to define a range or level of confidence (confidence interval) around an estimate. For instance, the 90 percent confidence level means that if all possible samples were selected and an estimate of a value and its sampling error were computed for each, then for approximately 90 percent of the samples, the intervals from 1.6 standard errors below the estimate to 1.6 standard errors above the estimate would include the "true" average value. For example, 82 percent of all State and local government workers in 2007 had early retirement benefits available with a standard error of 1.2 percentage points for this estimate. At the 90-percent level, the confidence interval for this estimate is from 80.1 to 83.9 percent or 82 percent plus or minus 1.9 percentage points (1.6 standard errors times 1.2 percentage points.)

The chances are about 68 out of 100 percent that an estimate from the survey differs from the true population figure within one standard error. The chances are about 90 out of 100 percent that this difference would be within 1.6 standard errors. This means that in the example above, the chances are 90 out of 100 percent that estimated early retirement benefits availability to State and local government workers is between 80.1 to 83.9 percent.

Comparative statements appearing in NCS benefit publications are statistically significant at the 90 percent level of confidence, unless otherwise indicated. This means that for differences cited, the estimated difference is greater than 1.6 times the standard error of the difference.